The teachers union is pitting its members against cops — by sponsoring and promoting the Rev. Al Sharpton’s anti-police rally in Staten Island next week, The Post has learned.

The United Federation of Teachers sent an “action alert” ­e-mail that even promised free transportation to Sharpton’s Aug. 23 demonstration that is billed as a march for justice for “victims of police brutality.”

Some teachers were furious that the union would take such a prominent role in the event.

“What a disgrace. What is going on with the leadership of the UFT thinking it’s OK to protest against rank-and-file cops?” asked one teacher. “Would we want cops protesting in front our schools over low test scores?”

Sharpton’s National Action Network, the NAACP and local 1199 SEIU — a strong supporter of Mayor de Blasio — are also members of the coalition.

But the mayor won’t be attending the protest. He had earlier cautioned organizers against attempting to march en masse across the bridge, which has no pedestrian walkway.

“Mr. Garner’s death was a tragedy for the city,” UFT President Michael Mulgrew said when asked about the union’s involvement. “Teachers want to help ensure that something like this doesn’t happen again.”

March organizers said the union is not helping fund transportation across the Verrazano Bridge from Brooklyn.

One top NYPD union leader said he’s troubled by the UFT’s actions. “Mulgrew is always on the wrong side of the issues, and I’m not surprised,” said Ed Mullins, head of the police sergeants union. “The UFT has other issues. This is not their issue.”

A flier for the rally — attached to a UFT e-mail sent to its membership — proclaims the rally a ”March for Justice for Victims of Police Brutality!”

It adds: “We Will Not Go Back.”

This wouldn’t be the first time the teachers union rallied against police action.

Five hundred of its members joined a June 2012 march protesting the city’s unequal implementation of stop-and-frisk.